Uniformly Distributed Measures have Big Pieces of Lipschitz Graphs locally
Metric Geometry
2018-03-26 v2
Abstract
The study of uniformly distributed measures was crucial in Preiss' proof of his theorem on rectifiability of measures with positive density. It is known that the support of a uniformly distributed measure is an analytic variety. In this paper, we provide quantitative information on the rectifiability of this variety. Tolsa had already shown that -uniform measures have Big Pieces of Lipschitz Graphs(BPLG) . Here, we prove that a uniformly distributed measure has BPLG locally.
Keywords
Cite
@article{arxiv.1603.03415,
title = {Uniformly Distributed Measures have Big Pieces of Lipschitz Graphs locally},
author = {A. Dali Nimer},
journal= {arXiv preprint arXiv:1603.03415},
year = {2018}
}